Given the parametric equations $x=t^2$ and $y=t+1$, eliminate the parameter to find a Cartesian equation of the curve.

• A. $y=\sqrt{x}+1$
• B. $y=x^2+1$
• C. $x={y-1}^2$
• D. $x=y+1$

Answer: (C)

Verified step by step guidance

1. Start with the given parametric equations: \(x = t^{2}\) and \(y = t + 1\).
2. Express the parameter \(t\) in terms of \(y\) by rearranging the second equation: \(t = y - 1\).
3. Substitute this expression for \(t\) into the first equation to eliminate the parameter: \(x = (y - 1)^{2}\).
4. This substitution gives the Cartesian equation of the curve without the parameter \(t\).
5. The final Cartesian equation is \(x = (y - 1)^{2}\), which relates \(x\) and \(y\) directly.